Answer:
5x<50
Step-by-step explanation:
Answer:
Step-by-step explanation:
5n < 50 <--- subtracts 4 from both sides
n < 10 <--- divides both sides by 5
Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works
testing n=10, 4 + 5(10) = 4 + 50 = 54.
testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.
X < 10, proven, verified, correct
The product of 3m and 5r is 15mr True or False Explain...
Step-by-step explanation:
let's see....
3m × 5r = 15mr
15(m × r)
15mr.
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gallon of
2
17. Mr. Jackson owns a vegetable juice stand. At the end of the day, he has
juice left. He pours an equal amount of the remaining juice mixture into 6 glasses.
What amount of juice does Mr. Jackson pour into each glass?
1
A.
gallon
12
B.
1
3
gallon
C. 3 gallons
D. 12 gallons
Answer:
12 gallons
Step-by-step explanation:
Solve each of these equations. Explain or show your reasoning.
2(x+5)=3x+1
3y−4=6−2y
3(n+2)=9(6−n)
15 players for a softball team show up for a game: (a) How many ways are there to choose 10 players to take the field? 3003 (b) How many ways are there to assign the 10 positions by selecting players from the 15 people who show up? 3003 (c) Of the 15 people who show up, 5 are women. How many ways are there to choose 10 players to take the field if at least one of these players must be a woman?
Answer:
(a) 3003 ways
(b) 10897286400 ways
(c) 3002 ways
Step-by-step explanation:
Given
[tex]n = 15[/tex] --- 15 players
Solving (a) Ways of selecting 10 players.
This implies combination.
So, we have:
[tex]r=10[/tex]
Using:
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
We have:
[tex]^{15}C_{10} = \frac{15!}{(15-10)!10!}[/tex]
[tex]^{15}C_{10} = \frac{15!}{5!10!}[/tex]
Simplify
[tex]^{15}C_{10} = \frac{15*14*13*12*11*10!}{5!10!}[/tex]
[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5!}[/tex]
[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5*4*3*2*1}[/tex]
[tex]^{15}C_{10} = \frac{360360}{120}[/tex]
[tex]^{15}C_{10} = 3003[/tex]
Solving (b) Ways of assigning positions to 10 players.
This implies permutation.
So, we have:
[tex]r=10[/tex]
Using:
[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]
We have:
[tex]^{15}P_{10} = \frac{15!}{(15-10)!}[/tex]
[tex]^{15}P_{10} = \frac{15!}{5!}[/tex]
Solve each factorial
[tex]^{15}P_{10} = \frac{1307674368000}{120}[/tex]
[tex]^{15}P_{10} = 10897286400[/tex]
Solving (c) Ways of choosing at least 1 woman
We have:
[tex]Men = 10[/tex]
[tex]Women = 5[/tex]
Ways of selecting 10 players is: (a) 3003 ways
Since the number of men are 10, there is 1 way of selecting 10 men (i.e. selection without women)
Using complement rule:
At least 1 woman = Total - No woman
[tex]At\ least\ 1\ woman = 3003 - 1[/tex]
[tex]At\ least\ 1\ woman = 3002[/tex]
HELP PLZ!
The Fluffy Lump Cat Toy Company rents a warehouse facility. There
is a fixed cost of $1200 a month for rent and a variable cost of $5 per box of
toys that are stored. If the total cost for this month was $1315, how many boxes
of toys are being stored?
NO LINKS
Answer:
23 boxes of toys are being stored.
Step-by-step explanation:
There is a fixed cost of $1200 a month for rent and a variable cost of $5 per box of toys that are stored
This means that for x boxes of toys stored, the total cost is of:
[tex]C(x) = 1200 + 5x[/tex]
If the total cost for this month was $1315, how many boxes of toys are being stored?
This is [tex]x[/tex] for which [tex]C(x) = 1315[/tex]. So
[tex]C(x) = 1200 + 5x[/tex]
[tex]1315 = 1200 + 5x[/tex]
[tex]5x = 115[/tex]
[tex]x = \frac{115}{5}[/tex]
[tex]x = 23[/tex]
23 boxes of toys are being stored.
A culture of bacteria has an initial population of 470 bacteria and doubles every 8 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 7 hours, to the nearest whole number?
Answer:
Step-by-step explanation:
The population of bacteria in the culture after 7 hours is approximately 883.
What is an exponential function?Several real-world phenomena, including population expansion, radioactive decay, compound interest, and the spread of diseases, are modeled using exponential functions. In calculus, where they are used to define the exponential and logarithmic functions—essential ideas in calculus and other fields of mathematics—they also play a significant role.
Using the formula [tex]P_t = P_0 \times 2^{\frac{t}{d}}[/tex], where P_t is the population after t hours, P₀ is the initial population, t is the time in hours and d is the doubling time, we can find the population of bacteria in the culture after 7 hours as follows:
Since the initial population is 470, we have P₀ = 470.
The doubling time is 8 hours, so we have d = 8.
Substituting these values into the formula, we get:
[tex]P_7 = 470 \times 2^{\frac{7}{8}}[/tex]
P₇≈ 882.77
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please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
#8 is one #9 is 4
Step-by-step explanation:
A box contains 7 blue socks, 13 yellow socks and 5 green socks. What is the probability of choosing a green sock at random?
1/5
1/7
5/21
5/20
Answer:
1/5
Step-by-step explanation:
7 + 13 =20
20 + 5 = 25
5 is a fifth of 25
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
There are 25 socks in total, only 5 of these are green.
The proportion would look like this:
[tex]\frac{5}{25}=\frac{1}{5}[/tex]
Graph the line with slope -1/2 passing through the point (-1,-2)
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]m = -\frac{1}{2}[/tex]
[tex](x_1,y_1) = (-1,2)[/tex]
Required
Graph the line
First, is to determine the equation of the line using:
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
So:
[tex]-\frac{1}{2} = \frac{y - 2}{x - -1}[/tex]
[tex]-\frac{1}{2} = \frac{y - 2}{x +1}[/tex]
[tex]\frac{-1}{2} = \frac{y - 2}{x +1}[/tex]
Cross multiply:
[tex](y -2) * 2 = -1 * (x + 1)[/tex]
[tex](y -2) * 2 = -x -1[/tex]
Solve for y - 2
[tex]y -2 = -\frac{x}{2} -\frac{1}{2}[/tex]
Solve for y
[tex]y = -\frac{x}{2} -\frac{1}{2} + 2[/tex]
[tex]y = -\frac{x}{2} +\frac{-1+4}{2}[/tex]
[tex]y = -\frac{x}{2} +\frac{3}{2}[/tex]
The above equation will then be plotted on the graph (See attachment)
Someone please help with this!!!!
Answer:
18. h = 14.4
19. h = 4.23
20. h = 15.28
21. h = 11.46
All answers are rounded to two decimal places.
Step-by-step explanation:
18. To find the height if you know all 3 sides. Multiply sides a & b, and divide the product by c.
x = (a * b)/c
x = (18 * 24)/30
x = 432/30
x = 72/5
x = 14.4
19. We know that the entire length of the hypotenuse is 27. However, 24 is needed here. That's 8/9 of 27, so 80 degrees is one of the angles. So we need to find the hypotenuse first. That can be done like this: b/sin(β)
24/sin(80)
24/0.98480775
24/1 * 4000000/3939231
8/1 * 4000000/1313077
32000000/1313077
24.3702388
Now to find the first leg, which will be the height of the entire triangle.
x = √c² - b²
x = √24.3702388² - 24²
x = √593.908539 - 576
x = √17.908539
x = 4.23184818
x = 4.23
20. This one requires similar work to #19, but the hypotenuse of the smaller triangle is x.
20/sin(60)
20/0.8660254
20/1 * 5000000/4330127
100000000/4330127
23.0940109
√23.0940109² - 20²
√533.333339 - 400
√133.333339
11.5470056
î The answer above is leg 2 of the smaller triangle.
x = √10² + 133.333339
x = √100 + 133.333339
x = √233.33339
x = 15.2752525
x = 15.28
21. There is no need to figure out what the height is. The entire triangle is 45-45-90.
x = (√18² + 18²) - 15
x = (√324 + 324) - 15
x = (√648) - 15
x = 25.46 - 15
x = 11.46
If 2^2x = 2^3, what is the value of x?
Answer:
X = 2 If the exponent 2 in the 2 does not have the x
Step-by-step explanation:
Evaluate the algebraic expression 3f + g,when f = 6, g = 8, h = 12 and j = 2
Simplify 1/4^-2 x 1/4^-7
If the area of a right-angled triangle is 47 56 cm and its height is 11.6 cm. finds its base.
Answer:
820
Step-by-step explanation:
Hi so if your area is 4756, the base would be 820
56,316 divided by 6 need step by step instructions
Answer:
9,386
Step-by-step explanation:
56,316 ÷ 6 = 9,386
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Convert the fraction 6/10 to a decimal.
Answer:
0.60
Step-by-step explanation:
Answer:
.60
Step-by-step explanation:
What is the angle of X
Answer:
∡x°=35°
Step-by-step explanation:
x° and 35° are vertical angles, so they are congruent to each other. Therefore, the measure of angle x° is also 35°
Rectangle is graphed in the coordinate plane. The following are the vertices of the rectang A(- 2, 2), B(6, 2), C(6, 3) and D(- 2, 3) . What is the area of rectangle ABCD?
Answer:
Adenosine triphosphate
Answer:
The area of the rectangle ABCD will be 8 sq. units.
Step-by-step explanation:
The rectangle shape ABCD has vertices A(- 2,2), B(6,2), C(6,3) and D(- 2,3).
Presently, length of side AB = [6 - (- 2)] = 8 units.
{Since the line AB is corresponding to the x-pivot, so the length of the portion AB will be the contrast between the x-directions of the focuses An and B}
Once more, line BC is corresponding to y-pivot and thus the length BC = (3 - 2) = 1 units.
Subsequently, the space of the square shape ABCD will be (8 × 1) = 8 sq. units. (Answer)
what is the y-intercept of the line that goes through (0, 0) (6, 3)
Answer:
QUESTION:
what is the y-intercept of the line that goes through (0, 0) (6, 3)
ANSWER:
Use the slope formula and the slope-intercept form to find the slope m and y-intercept b .
Slope: 1/2
y-intercept: (0,0)
Step-by-step explanation:
Hope that this helps you out! :)
If you have any questions please put them in the comment section below this answer.
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you.
A) 120
B) 125
C) 50
D) 100
Explain please answer
Answer:
69.08
Step-by-step explanation:
2×3.14=6.28
6.28×11=69.08
its worth 25 please help and show work
9514 1404 393
Answer:
3) y = √10
4) x = 5√2
Step-by-step explanation:
The side ratios of an isosceles right triangle (one of the "special" right triangles) are ...
1 : 1 : √2
So, for some multiplier k, they can be made to match the sides in your triangles.
__
3) 1·k : 1·k : k√2 = √5 : √5 : y
Clearly, k = √5, so ...
y = (√5)(√2)
y = √10
__
4) k : k : k√2 = x : x : 10
k = 10/√2 = (5√2)/2
k = x = (5√2)/2
find the value of x.
Answer:
5
Step-by-step explanation:
5y+155=180
5y=180-155=25
y=5
5y+13x=90
13x=90-25=65
x=5°
What does an individual's effective tax rate indicate?
A.
the average income earned
B.
the average tax rate
C.
the minimum tax rate
D.
the next year's tax rate
Answer:
d
Step-by-step explanation:
if the taxes raise each year
On the unit circle, an arc of length 2 subtends an angle, β. What is the radian measure of β?
Answer:
[tex](d)\ \beta = 2\ rad[/tex]
Step-by-step explanation:
Given
[tex]L =2[/tex] -- length of the arc
[tex]r = 1[/tex] --- radius of a unit circle
[tex]\beta =[/tex] the subtended angle
Required
Find [tex]\beta[/tex]
The length of an arc is:
[tex]L = r * \beta[/tex]
This gives:
[tex]2 = 1 * \beta[/tex]
[tex]2 = \beta[/tex]
Make [tex]\bets[/tex][tex]\beta[/tex] the subject
[tex]\beta = 2[/tex]
Hence:
[tex]\beta = 2\ rad[/tex]
Answer:
2rad
Step-by-step explanation:
Find the surface area of the cylinder and round to the nearest tenth.
6.If Addison types at a constant rate of 2 pages per hour, how many hours will it take to
type a paper that is 5 pages long?Immersive Reader
(20 Points)
0.4 hour
2.5 hours
5 hours
10 hours
Answer:
2.5 hours
Step-by-step explanation
it takes 1/2 a hour to write one page so do
5 x 1/2 which is 2.5 since there are 5 pages
A graph shows the survey results for a group of students who
were asked how many honors classes they have taken and
how many elective classes:
Class Choices
Number of Elective Classes
0
lo 1 2 3
4
5 6 7 8
9 10 11
Number of Honors Classes
How many elective classes would students likely have taken if
they have taken 12 honors classes? (4 points)
Helpppppppppppppppppppppppp
Answer:
[tex]x = 15[/tex]165+x = 180 (linear pair)
Hence x = 15
Solve -5x < -35. Enter your answer as an inequality.
Answer:
x > 7
Step-by-step explanation:
-5x < -35
(Divide by 5)
-x < -7
(When dividing by a negative number, you flip the sign)
x > 7
The answer of given inequality is x > 7 .
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
Given,
-5x < -35
Divide by 5 in inequality
-x < -7
Multiply by (-1) in inequality [flip the sign of inequality]
So, x > 7
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